response_id stringlengths 15 19 | problem_id stringlengths 6 10 | task_type stringclasses 4 values | score float64 0.9 1 | messages listlengths 2 2 |
|---|---|---|---|---|
vfm_705231_EUZn2ODJ | vfm_705231 | verifiable_math | 1 | [
{
"content": "Given an arithmetic-geometric sequence {a_n} with the first term of 2 and a common ratio of -1/3. The sum of its first n terms is denoted as S_n. If for any n∈N*, there's always A≤3S_n - 1/S_n≤B, find the minimum value of B-A.\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', whe... |
jdg_32789_BAmbyDuS | jdg_32789 | llm_judgeable_groundtruth_similarity | 0.98 | [
{
"content": "\nBelow is an instruction to modify a code file along with the code file. Apply these instructions and return the adapted code:\n\nInstruction:\nRefactor the RemoveNCMNodes function in the ncm.go file by removing the const RemoveNodeEndpoint and the getRemoveNCMNodesRequest function. Integrate the... |
vfm_170435_MbczHIGT | vfm_170435 | verifiable_math | 1 | [
{
"content": "Calculate $(\\sqrt[4]{16})^{12}$.\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where <answer> is the number or mathematical expression of the solution.",
"role": "user"
},
{
"content": "<think>Okay, so I need to calculate (fourth root of 16) raised to the 12th po... |
vfm_474806_RlgpUGCT | vfm_474806 | verifiable_math | 1 | [
{
"content": "Two congruent cones with radius 12 cm and height 12 cm are enclosed within a cylinder. The base of each cone is a base of the cylinder, and the height of the cylinder is 24 cm. What is the number of cubic centimeters in the volume of the cylinder not occupied by the cones? Express your answer in t... |
vfm_616359_I4qtMpKK | vfm_616359 | verifiable_math | 1 | [
{
"content": "There are 2020 quadratic equations written on the board:\n\n$$\n\\begin{gathered}\n2020 x^{2}+b x+2021=0 \\\\\n2019 x^{2}+b x+2020=0 \\\\\n2018 x^{2}+b x+2019=0 \\\\\n\\ldots \\\\\nx^{2}+b x+2=0\n\\end{gathered}\n$$\n\n(each subsequent equation is obtained from the previous one by decreasing the l... |
vfm_424742_gH2oKA7H | vfm_424742 | verifiable_math | 1 | [
{
"content": "Let \\\\(f(n)=2+{2}^{4}+{2}^{7}+{2}^{10}+\\ldots+{2}^{3n+10} (n\\in\\mathbb{N})\\\\), then \\\\(f(n)\\\\) equals to ( )\nA: \\\\(\\dfrac{2}{7}\\left({8}^{n}-1\\right) \\\\)\nB: \\\\(\\dfrac{2}{7}\\left({8}^{n+1}-1\\right) \\\\)\nC: \\\\(\\dfrac{2}{7}\\left({8}^{n+3}-1\\right) \\\\)\nD: \\\\(\\dfr... |
vfm_259144_UdpPCzhf | vfm_259144 | verifiable_math | 1 | [
{
"content": "Austin is putting stickers in a sticker book. He put 8 stickers on the first page, some stickers on the second page, 24 stickers on the third page, and 32 stickers on the fourth page. If this pattern continues, Austin will put 40 stickers on the fifth page. How many stickers did Austin put on the ... |
jdg_50882_E8YK6LYb | jdg_50882 | llm_judgeable_groundtruth_similarity | 1 | [
{
"content": "\nBelow is an instruction to modify a code file along with the code file. Apply these instructions and return the adapted code:\n\nInstruction:\nModify the `FilterInterceptor` class in `FilterInterceptor.cs` to add a null check for `DbContext` before executing the filter. Ensure that the code hand... |
jdg_264603_9WylQmPp | jdg_264603 | llm_judgeable_groundtruth_similarity | 0.95 | [
{
"content": "\nBelow is a question asked on the forum Stackoverflow.com. Provide a good and informational response to it like a helpful human would.\n\nQuestion:\nI'm doing a project called \"2D Shape editor\" in f#. I have done this project in c# before so I've got all the logics for how to connect two shapes... |
vfm_540054_oUQSRj4r | vfm_540054 | verifiable_math | 1 | [
{
"content": "If the least common multiple of $X$ and $Y$ is $180$, and the ratio of $X$ to $Y$ is $4:5$, find their greatest common divisor.\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where <answer> is the number or mathematical expression of the solution.",
"role": "user"
},
{... |
vfm_146313_WQie0UrA | vfm_146313 | verifiable_math | 1 | [
{
"content": "Given that the total surface area of a rectangular prism is 11, and the sum of the lengths of its twelve edges is 24, find the length of one of its space diagonals.\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where <answer> is the number or mathematical expression of the so... |
jdg_277245_eeFKSND7 | jdg_277245 | llm_judgeable_groundtruth_similarity | 0.95 | [
{
"content": "\nBelow is a question asked on the forum Stackoverflow.com. Provide a good and informational response to it like a helpful human would.\n\nQuestion:\nI am obtaining the path of template using paymenthtml = os.path.join(os.path.dirname(__file__), 'template\\\\payment.html') and calling it in anothe... |
vfm_412061_3x1GE5N3 | vfm_412061 | verifiable_math | 1 | [
{
"content": "Alice and Bob each think of a polynomial. Each of their polynomials is monic, has degree 5, and has the same positive constant term and the same coefficient of $x$. The product of their polynomials is \\[x^{10} + 4x^9 + 6x^8 + 4x^7 + 5x^6 + 10x^5 + 5x^4 + 6x^3 + 4x^2 + 4x + 9.\\] What is the const... |
vfm_566471_WuJ5HjEA | vfm_566471 | verifiable_math | 1 | [
{
"content": "Mike picked 7 apples , Nancy picked 3 apples , and Keith picked 6 apples and 4 pears , at the farm. In total , _____ apples were picked .\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where <answer> is the number or mathematical expression of the solution.",
"role": "user... |
vfm_139352_xlgSFSWc | vfm_139352 | verifiable_math | 1 | [
{
"content": "The price of electricity went up by 25%. John's old computer used 800 watts and his new computer uses 50% more. If the old price of electricity was a certain amount per kilowatt-hour, his computer costs $9 to run for 50 hours. What was the old price of electricity per kilowatt-hour?\n\nReturn your... |
vfm_508726_SkHEgtgg | vfm_508726 | verifiable_math | 1 | [
{
"content": "Given the function $f\\left( x \\right)=\\sin \\left( \\omega x+\\dfrac{\\pi }{6} \\right)$ ($\\omega > 0$), the equation of one symmetric axis of the graph is $x=\\dfrac{\\pi }{12}$. What is the minimum value of $\\omega$?\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where ... |
vfc_45621_SKVmqHbY | vfc_45621 | verifiable_code | 1 | [
{
"content": "Solve the following coding problem using the programming language python:\n\nThere are n games in a football tournament. Three teams are participating in it. Currently k games had already been played. \n\nYou are an avid football fan, but recently you missed the whole k games. Fortunately, you rem... |
vcu_3050_7nS9IrT2 | vcu_3050 | code_output_prediction | 1 | [
{
"content": "\nBelow you are given code written in python that contains the function 'stuff', which manipulates a string, as well as an input to the function. Your job is to predict the output of 'stuff' given the provided input.\n\nHere is the code:\n```python\ndef stuff(a: str) -> str:\n from functools im... |
jdg_130321_sd0vKKyf | jdg_130321 | llm_judgeable_groundtruth_similarity | 0.95 | [
{
"content": "\nBelow is a question asked on the forum math.stackexchange.com. Provide a good and informational response to it like a helpful human would.\n\nQuestion:\nFind the remainder of $2^n+n^2$ modulus 6 given that $2^n+n^2$ is a prime and $n\\geq2$($n$ positive integer) I tried to solve this but failed!... |
vfm_282782_X3r55Rkr | vfm_282782 | verifiable_math | 1 | [
{
"content": "Compute $\\gcd(83^9+1,83^9+83^2+1)$.\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where <answer> is the number or mathematical expression of the solution.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the greatest common divisor (gcd) of two ... |
vfm_591903_LhDsIB3p | vfm_591903 | verifiable_math | 1 | [
{
"content": "Caleb invested Rs. 2500 at 79 to obtain a certain income from his stock. The dividend is 6.32. What is the income Caleb obtained from his stock?\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where <answer> is the number or mathematical expression of the solution.",
"role"... |
vfm_573707_Ed6vAtvF | vfm_573707 | verifiable_math | 1 | [
{
"content": "Let x be the original price per kilo of rice. If this price falls by 25%, and previously you could buy 30 kg with a certain amount of money, how much rice in kilograms can you buy now with the same amount?\n\nReturn your final response as 'Final Answer: \\boxed{<answer>}', where <answer> is the nu... |
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